Author:
McKnight J. D.,Musser Gary L.
Abstract
In [3], the study of (p;q) radicals was initiated. In this paper, the integral polynomials p(x) and q(x) which determine the Jacobson radical are characterized and the Jacobson radical is shown to be the only semiprime (p;q) radical for which all fields are semisimple. Also, it is observed that the prime, nil, and Brown-McCoy radicals are not (p;q) radicals. To show that the semiprime (p;q) radicals are special and that they can be determined by subclasses of the class of primitive rings, a classification theorem for (p;q)-regular primitive rings is given. Finally, it is shown that the collection of semiprime (p;q) radicals and the collection of semiprime (p;1) radicals coincide.
Publisher
Canadian Mathematical Society
Cited by
3 articles.
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1. Pseudoregular radical classes;Bulletin of the Australian Mathematical Society;2001-12
2. Associative rings;Journal of Soviet Mathematics;1980-07
3. A class of regularities for rings;Journal of the Australian Mathematical Society;1979-06